subject verb agreement - Conjunction reduction

Is this sentence grammatically correct?

It is common for a native American who has never driven a car to move to another part of the country and have to learn to do it.

My guess is that the sentence is wrong because in this part: "have to learn to do it", "have" must agree with the subject, i.e. "a native American", which is singular. Hence, it should be "has to learn to do it".

Answer

It is correct as written. "Have" is an infinitive in this case.

We can reduce the sentence like this:

It is common for an American to have to learn this.

In the full sentence, "and" makes the "to" before "move" apply to "have" also.

You could also write "...and to have to learn..."